This dataset is the first observational data release for the JWST Early Release Science Ice Age program (#1309). More information about this program can be found at our team website (http://jwst-iceage.org/) and the STScI website (https://www.stsci.edu/jwst/science-execution/approved-programs/dd-ers/program-1309). The data is analyzed in the article by McClure et al. (2023), to be published on January 24th, 2023 by Nature Astronomy. The dataset consists of 5 files, each containing a spectrum of one of two background stars analyzed in that publication. The spectra are given as wavelength in microns (column 1), flux in milli-Janskys (column 2), and uncertainty in the flux (column 3). Some basic information about the JWST pipeline version is given in the header of each text file, but users should refer to the Methods section of McClure et al. (2023) for the full description of how the data were processed and extracted, as it extends beyond the basic pipelines. Information about how the data were observed is given in the APT file, accessible through a query in STScI's APT application (search by PID 1309) or here at STScI (https://www.stsci.edu/jwst/science-execution/program-information.html?id=1309). Three of the files correspond to the background star NIR38. These represent spectra of this star taken separately by JWST with the NIRCam WFSS, NIRSpec FS, and MIRI LRS FS instrument modes on JWST. The other two files correspond to the background star J110621 and are spectra taken separately by JWST using the NIRSpec FS and MIRI LRS FS instrument modes. It is necessary to cite the McClure et al. (2023) Nature Astronomy publication when making use of these data, to fully describe the data processing, as well as this Zenodo DOI.